(1)) The equation of line p is y+7=-(1)/(2)(x-5) Line q is parallel to line p and passes through (4,8) What is the equation of line q?

To find the equation of line q, we need to use the point-slope form of a linear equation, which is given by:<br /><br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.<br /><br />Since line q is parallel to line p, it will have the same slope as line p. The slope of line p can be found by rearranging the equation of line p in slope-intercept form (i.e., $y = mx + b$), where $m$ is the slope and $b$ is the y-intercept.<br /><br />Rearranging the equation of line p, we have:<br /><br />$y = -\frac{1}{2}(x - 5) - 7$<br /><br />Simplifying further, we get:<br /><br />$y = -\frac{1}{2}x + \frac{5}{2} - 7$<br /><br />$y = -\frac{1}{2}x - \frac{9}{2}$<br /><br />From this equation, we can see that the slope of line p is $-\frac{1}{2}$.<br /><br />Now, we can use the point-slope form to find the equation of line q. We know that line q passes through the point $(4, 8)$, so we can substitute these values into the point-slope form:<br /><br />$y - 8 = -\frac{1}{2}(x - 4)$<br /><br />Simplifying further, we get:<br /><br />$y - 8 = -\frac{1}{2}x + 2$<br /><br />$y = -\frac{1}{2}x + 10$<br /><br />Therefore, the equation of line q is $y = -\frac{1}{2}x + 10$.